Waiting Times

[Pages:38]Waiting Times

Chapter 7

These slides are based in part on slides that come with Cachon & Terwiesch book Matching Supply with Demand . If you want to use these in your course, you may have to adopt the book as a textbook

or obtain permission from the authors Cachon & Terwiesch. 1

utdallas.edu/~metin

Learning Objectives

Interarrival and Service Times and their variability Obtaining the average time spent in the queue Pooling of server capacities Priority rules

utdallas.edu/~metin

2

Where are the queues?

utdallas.edu/~metin

3

A Queue is made of a server and a queue in front

Input:

Passengers in an airport Customers at a bank Patients at a hospital Callers at a call center

Arrival rate

Buffer

Queues

Processing

Resources:

Check-in clerks at an airport Tellers at a bank Nurses at a hospital Customer service representatives

(CRS) at a call center

Capacity

We are interested in the waiting times in the queue and the queue length.

utdallas.edu/~metin

An Example of a Simple Queuing System

Incoming calls

Calls on Hold

Reps processing

calls

Answered Calls

Call center

Blocked calls (busy signal)

Abandoned calls (tired of waiting)

At peak, 80% of calls dialed received a busy signal.

Customers getting through had to wait on average 10 minutes

Extra phone line expense per day for waiting was $25,000.

Financial consequences

Lost throughput

utdallas.edu/~metin

Holding cost Lost goodwill Lost throughput (abandoned)

Cost of capacity Cost per customer

$$$ Revenue $$$

5

A Somewhat Odd Service Process

Constant Arrival Rate (0.2/min) and Service Times (4 min)

Arrival rate 0.2/min = 1/(4 mins) = 1 every five minutes, which implies interarrival time of 5 minutes. Units of arrival rate 1/min whereas units of interarrival time is min.

Arrival Service

Patient Time

Time

1

0

4

2

5

4

3

10 4

4

15 4

5

20 4

6

25 4

7

30 4

8

35 4

9

40 4

10 45 4

11 50 4

12 55 4

utdallas.edu/~metin

7:00

7:10

7:20

7:30

7:40

7:50

8:00 6

Where is Variability?

There certainly is significant (actually infinite) amount of waiting when the arrival rate is greater than the service rate

? Equivalently, the processing capacity is less than the arrival rate

More interestingly, variability can cause long waiting times. Variability in

? Arrival process ? Processing times ? Availability of resources; Absent, sick, broken or vacationing servers. ? Types of customers; Priority versus regular customers. ? Routing of flow units; Recall the Resume Validation Example. ? Response of customers to waiting for a while; Wait more or abandon

utdallas.edu/~metin

7

Variability: Where does it come from? Examples

Tasks:

? Inherent variation ? Lack of Standard Operating Procedures ? Quality (scrap / rework)

Input:

Buffer

? Unpredicted Volume swings

? Random arrivals (randomness is the rule,

not the exception)

? Incoming quality

? Product Mix

Especially relevant in service operations (what is different in service industries?): ? emergency room ? air-line check in ? call center ? check-outs at cashier

utdallas.edu/~metin

Processing

Resources:

? Breakdowns / Maintenance ? Operator absence ? Set-up times

Routes:

? Variable routing ? Dedicated machines

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download